Related papers: The Origin of a Metric
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to…
This survey synthesizes the principal descriptive set-theoretic perspectives on deterministic Cantor sets on the real line and charts directions for future study. After recounting their historical genesis and compiling an up-to-date…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
With a view to establishing measure theoretic approximation properties of Delone sets, we study a setup which arises naturally in the problem of averaging almost periodic functions along exponential sequences. In this setting, we establish…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
In this paper, we study the metric theory of dyadic approximation in the middle-third Cantor set. This theory complements earlier work of Levesley, Salp, and Velani (2007), who investigated the problem of approximation in the Cantor set by…
In this letter we uncover a new facet of chiral symmetry and the implications of its breaking in some theories. By generalizing the concept of chiral symmetry, tensor theories naturally arise. This novel approach adds to the known uses of…
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
In the first part of this paper the notion of natural metric on the set of natural numbers is defined. It is such metric that the completion of N is a compact metric space that a probability borel measure exists in order that the sequence…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
Symmetry breaking is discussed in this paper which comes from the Lorentz transformation of special relativity and changes our view that two relatively moving bodies always have the relative speed equal in magnitude and opposite in…